Q.A $100\,\Omega$ resistor is connected to a 220 V, 50 Hz supply. Calculate:

When a resistor of resistance R is connected directly to an AC source $e=e_0\sin\omega t$, applying $e=iR$ instantaneously (Ohm's law holding at every instant, since a resistor's behaviour is not frequency-dependent) gives $i=\dfrac{e_0}{R}\sin\omega t=i_0\sin\omega t$, with peak current $i_0=e_0/R$. Comparing this with the applied emf shows current and voltage are described by the exact same sine function -- they are exactly IN PHASE, reaching zero, their peak, and their minimum simultaneously at every instant. …